Wasn't Marshall under a contract? How do they get out of paying his salary when he is under contract? Don't they have to break the contract somehow?

His Salary is based on him being on the team. If he's cut then he leaves with whatever he's already been paid and will look for another deal somewhere else. Normally any money that's guaranteed is paid out over the first 2-3 years of the contract in the form of Signing bonuses and/or Roster bonuses. If the player has unpaid guaranteed money still on the table than something will be worked out (AA was going into his 2nd year had $5M due from the Skins even though he was traded). Marshall was in the last year of his contract and no unpaid guaranteed money left in the contract.